Question

The regular gas price regular gas in the Lansing area is a normally distributed random variable with a mean of $2.35 and a coefficient of variation of 5%. What is the standard deviation? What is the probability that the price of gas will be between $2.01 (lowest price in Lansing as of 2/11 –at 5200 S Pennsylvania Ave & Simms Ct) and $2.30?

Answer 1

Sol:

mean=2.35

cv=5%

cv=sd/mean*100

sd=cv*mean=5*2.35

sd=11.75

s the standard deviation=11.75

P(2.01<x<2.03)

z=x-mean/sd

P(2.01-2.35/11.75<Z<2.03-2.35/11.75)

P(-0.0289<z<-0.0272)

=P(z<-0.0272)-P(z<-0.0289)

=0.4891-0.4885

From standard normal table

=0.0007

standard deviation=11.75

the probability that the price of gas will be between $2.01 (lowest price in Lansing as of 2/11 –at 5200 S Pennsylvania Ave & Simms Ct) and $2.30 is 0.0007